论文标题
Laguerre Beta合奏的日志决定因素的边缘CLT
An edge CLT for the log determinant of Laguerre beta ensembles
论文作者
论文摘要
我们获得了$ \ log | \ det（m_n-s_n）| $的CLT，其中$ m_n $是一个缩放的laguerre $β$集合和$ s_n = d _ ++σ_nn^n^n^{ - 2/3} $，带有$ d _+$ $ d _+$表示$ m_n $ a $ a $ a $ a $ a $ a $ = n $ a n $ = n $ n $ = n \llσ_n\ ll \ log^2 n $）。在Lue和Loe的特殊情况下，我们证明CLT还以$σ_n$的恒定顺序持有。 Johnstone，Klochkov，Onatski和Pavlyshyn证明了Wigner矩阵的类似结果。获得这种类型的Laguerre矩阵CLT对于在临界温度下进行批判性尖刺样品协方差矩阵以及两部分球形旋转玻璃的自由能的统计测试。
We obtain a CLT for $\log|\det(M_n-s_n)|$ where $M_n$ is a scaled Laguerre $β$ ensemble and $s_n=d_++σ_n n^{-2/3}$ with $d_+$ denoting the upper edge of the limiting spectrum of $M_n$ and $σ_n$ a slowly growing function ($\log\log^2 n\llσ_n\ll\log^2 n$). In the special cases of LUE and LOE, we prove that the CLT also holds for $σ_n$ of constant order. A similar result was proved for Wigner matrices by Johnstone, Klochkov, Onatski, and Pavlyshyn. Obtaining this type of CLT of Laguerre matrices is of interest for statistical testing of critically spiked sample covariance matrices as well as free energy of bipartite spherical spin glasses at critical temperature.
